Information on Result #1529399
Linear OOA(3213, 4194515, F3, 3, 19) (dual of [(4194515, 3), 12583332, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3213, 4194515, F3, 2, 19) (dual of [(4194515, 2), 8388817, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(332, 214, F3, 2, 9) (dual of [(214, 2), 396, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(332, 214, F3, 9) (dual of [214, 182, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(332, 255, F3, 9) (dual of [255, 223, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(331, 244, F3, 9) (dual of [244, 213, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 244 | 310−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(321, 244, F3, 7) (dual of [244, 223, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 244 | 310−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(332, 255, F3, 9) (dual of [255, 223, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(332, 214, F3, 9) (dual of [214, 182, 10]-code), using
- linear OOA(3181, 4194301, F3, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
- linear OOA(332, 214, F3, 2, 9) (dual of [(214, 2), 396, 10]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3213, 2097257, F3, 5, 19) (dual of [(2097257, 5), 10486072, 20]-NRT-code) | [i] | OOA Folding | |